intersection of diagonals of parallelogram lies on a diagonal of convex ABCD
Source: 2022 Oral Moscow Geometry Olympiad grades 10-11 p3
April 18, 2022
geometryparallelogramcollinear
Problem Statement
Extensions of opposite sides of a convex quadrilateral intersect at points and . Points are marked on the sides of (one per side), which are the vertices of a parallelogram with a side parallel to . Prove that the intersection point of the diagonals of this parallelogram lies on one of the diagonals of quadrilateral .(E. Bakaev)